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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St000807
-----------------------------------------------------------------------------
Collection: Integer compositions
-----------------------------------------------------------------------------
Description: The sum of the heights of the valleys of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. A valley is a contiguous subsequence consisting of an up step, a sequence of horizontal steps, and a down step. This statistic is the sum of the heights of the valleys.
-----------------------------------------------------------------------------
References: [1] Deutsch, E., Elizalde, S. A bijection between bargraphs and Dyck paths [[arXiv:1705.05984]]
-----------------------------------------------------------------------------
Code:
def statistic(c):
v = 0
found_DH = False
for i in range(1,len(c)):
if found_DH:
if c[i] > c[i-1]:
found_DH = False
v += c[i-1]
else:
if c[i] < c[i-1]:
found_DH = True
return v
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[1,1] => 0
[2] => 0
[1,1,1] => 0
[1,2] => 0
[2,1] => 0
[3] => 0
[1,1,1,1] => 0
[1,1,2] => 0
[1,2,1] => 0
[1,3] => 0
[2,1,1] => 0
[2,2] => 0
[3,1] => 0
[4] => 0
[1,1,1,1,1] => 0
[1,1,1,2] => 0
[1,1,2,1] => 0
[1,1,3] => 0
[1,2,1,1] => 0
[1,2,2] => 0
[1,3,1] => 0
[1,4] => 0
[2,1,1,1] => 0
[2,1,2] => 1
[2,2,1] => 0
[2,3] => 0
[3,1,1] => 0
[3,2] => 0
[4,1] => 0
[5] => 0
[1,1,1,1,1,1] => 0
[1,1,1,1,2] => 0
[1,1,1,2,1] => 0
[1,1,1,3] => 0
[1,1,2,1,1] => 0
[1,1,2,2] => 0
[1,1,3,1] => 0
[1,1,4] => 0
[1,2,1,1,1] => 0
[1,2,1,2] => 1
[1,2,2,1] => 0
[1,2,3] => 0
[1,3,1,1] => 0
[1,3,2] => 0
[1,4,1] => 0
[1,5] => 0
[2,1,1,1,1] => 0
[2,1,1,2] => 1
[2,1,2,1] => 1
[2,1,3] => 1
[2,2,1,1] => 0
[2,2,2] => 0
[2,3,1] => 0
[2,4] => 0
[3,1,1,1] => 0
[3,1,2] => 1
[3,2,1] => 0
[3,3] => 0
[4,1,1] => 0
[4,2] => 0
[5,1] => 0
[6] => 0
[1,1,1,1,1,1,1] => 0
[1,1,1,1,1,2] => 0
[1,1,1,1,2,1] => 0
[1,1,1,1,3] => 0
[1,1,1,2,1,1] => 0
[1,1,1,2,2] => 0
[1,1,1,3,1] => 0
[1,1,1,4] => 0
[1,1,2,1,1,1] => 0
[1,1,2,1,2] => 1
[1,1,2,2,1] => 0
[1,1,2,3] => 0
[1,1,3,1,1] => 0
[1,1,3,2] => 0
[1,1,4,1] => 0
[1,1,5] => 0
[1,2,1,1,1,1] => 0
[1,2,1,1,2] => 1
[1,2,1,2,1] => 1
[1,2,1,3] => 1
[1,2,2,1,1] => 0
[1,2,2,2] => 0
[1,2,3,1] => 0
[1,2,4] => 0
[1,3,1,1,1] => 0
[1,3,1,2] => 1
[1,3,2,1] => 0
[1,3,3] => 0
[1,4,1,1] => 0
[1,4,2] => 0
[1,5,1] => 0
[1,6] => 0
[2,1,1,1,1,1] => 0
[2,1,1,1,2] => 1
[2,1,1,2,1] => 1
[2,1,1,3] => 1
[2,1,2,1,1] => 1
[2,1,2,2] => 1
[2,1,3,1] => 1
[2,1,4] => 1
[2,2,1,1,1] => 0
[2,2,1,2] => 1
[2,2,2,1] => 0
[2,2,3] => 0
[2,3,1,1] => 0
[2,3,2] => 0
[2,4,1] => 0
[2,5] => 0
[3,1,1,1,1] => 0
[3,1,1,2] => 1
[3,1,2,1] => 1
[3,1,3] => 1
[3,2,1,1] => 0
[3,2,2] => 0
[3,3,1] => 0
[3,4] => 0
[4,1,1,1] => 0
[4,1,2] => 1
[4,2,1] => 0
[4,3] => 0
[5,1,1] => 0
[5,2] => 0
[6,1] => 0
[7] => 0
[1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,2] => 0
[1,1,1,1,1,2,1] => 0
[1,1,1,1,1,3] => 0
[1,1,1,1,2,1,1] => 0
[1,1,1,1,2,2] => 0
[1,1,1,1,3,1] => 0
[1,1,1,1,4] => 0
[1,1,1,2,1,1,1] => 0
[1,1,1,2,1,2] => 1
[1,1,1,2,2,1] => 0
[1,1,1,2,3] => 0
[1,1,1,3,1,1] => 0
[1,1,1,3,2] => 0
[1,1,1,4,1] => 0
[1,1,1,5] => 0
[1,1,2,1,1,1,1] => 0
[1,1,2,1,1,2] => 1
[1,1,2,1,2,1] => 1
[1,1,2,1,3] => 1
[1,1,2,2,1,1] => 0
[1,1,2,2,2] => 0
[1,1,2,3,1] => 0
[1,1,2,4] => 0
[1,1,3,1,1,1] => 0
[1,1,3,1,2] => 1
[1,1,3,2,1] => 0
[1,1,3,3] => 0
[1,1,4,1,1] => 0
[1,1,4,2] => 0
[1,1,5,1] => 0
[1,1,6] => 0
[1,2,1,1,1,1,1] => 0
[1,2,1,1,1,2] => 1
[1,2,1,1,2,1] => 1
[1,2,1,1,3] => 1
[1,2,1,2,1,1] => 1
[1,2,1,2,2] => 1
[1,2,1,3,1] => 1
[1,2,1,4] => 1
[1,2,2,1,1,1] => 0
[1,2,2,1,2] => 1
[1,2,2,2,1] => 0
[1,2,2,3] => 0
[1,2,3,1,1] => 0
[1,2,3,2] => 0
[1,2,4,1] => 0
[1,2,5] => 0
[1,3,1,1,1,1] => 0
[1,3,1,1,2] => 1
[1,3,1,2,1] => 1
[1,3,1,3] => 1
[1,3,2,1,1] => 0
[1,3,2,2] => 0
[1,3,3,1] => 0
[1,3,4] => 0
[1,4,1,1,1] => 0
[1,4,1,2] => 1
[1,4,2,1] => 0
[1,4,3] => 0
[1,5,1,1] => 0
[1,5,2] => 0
[1,6,1] => 0
[1,7] => 0
[2,1,1,1,1,1,1] => 0
[2,1,1,1,1,2] => 1
[2,1,1,1,2,1] => 1
[2,1,1,1,3] => 1
[2,1,1,2,1,1] => 1
[2,1,1,2,2] => 1
[2,1,1,3,1] => 1
[2,1,1,4] => 1
[2,1,2,1,1,1] => 1
[2,1,2,1,2] => 2
[2,1,2,2,1] => 1
[2,1,2,3] => 1
[2,1,3,1,1] => 1
[2,1,3,2] => 1
[2,1,4,1] => 1
[2,1,5] => 1
[2,2,1,1,1,1] => 0
[2,2,1,1,2] => 1
[2,2,1,2,1] => 1
[2,2,1,3] => 1
[2,2,2,1,1] => 0
[2,2,2,2] => 0
[2,2,3,1] => 0
[2,2,4] => 0
[2,3,1,1,1] => 0
[2,3,1,2] => 1
[2,3,2,1] => 0
[2,3,3] => 0
[2,4,1,1] => 0
[2,4,2] => 0
[2,5,1] => 0
[2,6] => 0
[3,1,1,1,1,1] => 0
[3,1,1,1,2] => 1
[3,1,1,2,1] => 1
[3,1,1,3] => 1
[3,1,2,1,1] => 1
[3,1,2,2] => 1
[3,1,3,1] => 1
[3,1,4] => 1
[3,2,1,1,1] => 0
[3,2,1,2] => 1
[3,2,2,1] => 0
[3,2,3] => 2
[3,3,1,1] => 0
[3,3,2] => 0
[3,4,1] => 0
[3,5] => 0
[4,1,1,1,1] => 0
[4,1,1,2] => 1
[4,1,2,1] => 1
[4,1,3] => 1
[4,2,1,1] => 0
[4,2,2] => 0
[4,3,1] => 0
[4,4] => 0
[5,1,1,1] => 0
[5,1,2] => 1
[5,2,1] => 0
[5,3] => 0
[6,1,1] => 0
[6,2] => 0
[7,1] => 0
[8] => 0
[1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,2] => 0
[1,1,1,1,1,1,2,1] => 0
[1,1,1,1,1,1,3] => 0
[1,1,1,1,1,2,1,1] => 0
[1,1,1,1,1,2,2] => 0
[1,1,1,1,1,3,1] => 0
[1,1,1,1,1,4] => 0
[1,1,1,1,2,1,1,1] => 0
[1,1,1,1,2,1,2] => 1
[1,1,1,1,2,2,1] => 0
[1,1,1,1,2,3] => 0
[1,1,1,1,3,1,1] => 0
[1,1,1,1,3,2] => 0
[1,1,1,1,4,1] => 0
[1,1,1,1,5] => 0
[1,1,1,2,1,1,1,1] => 0
[1,1,1,2,1,1,2] => 1
[1,1,1,2,1,2,1] => 1
[1,1,1,2,1,3] => 1
[1,1,1,2,2,1,1] => 0
[1,1,1,2,2,2] => 0
[1,1,1,2,3,1] => 0
[1,1,1,2,4] => 0
[1,1,1,3,1,1,1] => 0
[1,1,1,3,1,2] => 1
[1,1,1,3,2,1] => 0
[1,1,1,3,3] => 0
[1,1,1,4,1,1] => 0
[1,1,1,4,2] => 0
[1,1,1,5,1] => 0
[1,1,1,6] => 0
[1,1,2,1,1,1,1,1] => 0
[1,1,2,1,1,1,2] => 1
[1,1,2,1,1,2,1] => 1
[1,1,2,1,1,3] => 1
[1,1,2,1,2,1,1] => 1
[1,1,2,1,2,2] => 1
[1,1,2,1,3,1] => 1
[1,1,2,1,4] => 1
[1,1,2,2,1,1,1] => 0
[1,1,2,2,1,2] => 1
[1,1,2,2,2,1] => 0
[1,1,2,2,3] => 0
[1,1,2,3,1,1] => 0
[1,1,2,3,2] => 0
[1,1,2,4,1] => 0
[1,1,2,5] => 0
[1,1,3,1,1,1,1] => 0
[1,1,3,1,1,2] => 1
[1,1,3,1,2,1] => 1
[1,1,3,1,3] => 1
[1,1,3,2,1,1] => 0
[1,1,3,2,2] => 0
[1,1,3,3,1] => 0
[1,1,3,4] => 0
[1,1,4,1,1,1] => 0
[1,1,4,1,2] => 1
[1,1,4,2,1] => 0
[1,1,4,3] => 0
[1,1,5,1,1] => 0
[1,1,5,2] => 0
[1,1,6,1] => 0
[1,1,7] => 0
[1,2,1,1,1,1,1,1] => 0
[1,2,1,1,1,1,2] => 1
[1,2,1,1,1,2,1] => 1
[1,2,1,1,1,3] => 1
[1,2,1,1,2,1,1] => 1
[1,2,1,1,2,2] => 1
[1,2,1,1,3,1] => 1
[1,2,1,1,4] => 1
[1,2,1,2,1,1,1] => 1
[1,2,1,2,1,2] => 2
[1,2,1,2,2,1] => 1
[1,2,1,2,3] => 1
[1,2,1,3,1,1] => 1
[1,2,1,3,2] => 1
[1,2,1,4,1] => 1
[1,2,1,5] => 1
[1,2,2,1,1,1,1] => 0
[1,2,2,1,1,2] => 1
[1,2,2,1,2,1] => 1
[1,2,2,1,3] => 1
[1,2,2,2,1,1] => 0
[1,2,2,2,2] => 0
[1,2,2,3,1] => 0
[1,2,2,4] => 0
[1,2,3,1,1,1] => 0
[1,2,3,1,2] => 1
[1,2,3,2,1] => 0
[1,2,3,3] => 0
[1,2,4,1,1] => 0
[1,2,4,2] => 0
[1,2,5,1] => 0
[1,2,6] => 0
[1,3,1,1,1,1,1] => 0
[1,3,1,1,1,2] => 1
[1,3,1,1,2,1] => 1
[1,3,1,1,3] => 1
[1,3,1,2,1,1] => 1
[1,3,1,2,2] => 1
[1,3,1,3,1] => 1
[1,3,1,4] => 1
[1,3,2,1,1,1] => 0
[1,3,2,1,2] => 1
[1,3,2,2,1] => 0
[1,3,2,3] => 2
[1,3,3,1,1] => 0
[1,3,3,2] => 0
[1,3,4,1] => 0
[1,3,5] => 0
[1,4,1,1,1,1] => 0
[1,4,1,1,2] => 1
[1,4,1,2,1] => 1
[1,4,1,3] => 1
[1,4,2,1,1] => 0
[1,4,2,2] => 0
[1,4,3,1] => 0
[1,4,4] => 0
[1,5,1,1,1] => 0
[1,5,1,2] => 1
[1,5,2,1] => 0
[1,5,3] => 0
[1,6,1,1] => 0
[1,6,2] => 0
[1,7,1] => 0
[1,8] => 0
[2,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,2] => 1
[2,1,1,1,1,2,1] => 1
[2,1,1,1,1,3] => 1
[2,1,1,1,2,1,1] => 1
[2,1,1,1,2,2] => 1
[2,1,1,1,3,1] => 1
[2,1,1,1,4] => 1
[2,1,1,2,1,1,1] => 1
[2,1,1,2,1,2] => 2
[2,1,1,2,2,1] => 1
[2,1,1,2,3] => 1
[2,1,1,3,1,1] => 1
[2,1,1,3,2] => 1
[2,1,1,4,1] => 1
[2,1,1,5] => 1
[2,1,2,1,1,1,1] => 1
[2,1,2,1,1,2] => 2
[2,1,2,1,2,1] => 2
[2,1,2,1,3] => 2
[2,1,2,2,1,1] => 1
[2,1,2,2,2] => 1
[2,1,2,3,1] => 1
[2,1,2,4] => 1
[2,1,3,1,1,1] => 1
[2,1,3,1,2] => 2
[2,1,3,2,1] => 1
[2,1,3,3] => 1
[2,1,4,1,1] => 1
[2,1,4,2] => 1
[2,1,5,1] => 1
[2,1,6] => 1
[2,2,1,1,1,1,1] => 0
[2,2,1,1,1,2] => 1
[2,2,1,1,2,1] => 1
[2,2,1,1,3] => 1
[2,2,1,2,1,1] => 1
[2,2,1,2,2] => 1
[2,2,1,3,1] => 1
[2,2,1,4] => 1
[2,2,2,1,1,1] => 0
[2,2,2,1,2] => 1
[2,2,2,2,1] => 0
[2,2,2,3] => 0
[2,2,3,1,1] => 0
[2,2,3,2] => 0
[2,2,4,1] => 0
[2,2,5] => 0
[2,3,1,1,1,1] => 0
[2,3,1,1,2] => 1
[2,3,1,2,1] => 1
[2,3,1,3] => 1
[2,3,2,1,1] => 0
[2,3,2,2] => 0
[2,3,3,1] => 0
[2,3,4] => 0
[2,4,1,1,1] => 0
[2,4,1,2] => 1
[2,4,2,1] => 0
[2,4,3] => 0
[2,5,1,1] => 0
[2,5,2] => 0
[2,6,1] => 0
[2,7] => 0
[3,1,1,1,1,1,1] => 0
[3,1,1,1,1,2] => 1
[3,1,1,1,2,1] => 1
[3,1,1,1,3] => 1
[3,1,1,2,1,1] => 1
[3,1,1,2,2] => 1
[3,1,1,3,1] => 1
[3,1,1,4] => 1
[3,1,2,1,1,1] => 1
[3,1,2,1,2] => 2
[3,1,2,2,1] => 1
[3,1,2,3] => 1
[3,1,3,1,1] => 1
[3,1,3,2] => 1
[3,1,4,1] => 1
[3,1,5] => 1
[3,2,1,1,1,1] => 0
[3,2,1,1,2] => 1
[3,2,1,2,1] => 1
[3,2,1,3] => 1
[3,2,2,1,1] => 0
[3,2,2,2] => 0
[3,2,3,1] => 2
[3,2,4] => 2
[3,3,1,1,1] => 0
[3,3,1,2] => 1
[3,3,2,1] => 0
[3,3,3] => 0
[3,4,1,1] => 0
[3,4,2] => 0
[3,5,1] => 0
[3,6] => 0
[4,1,1,1,1,1] => 0
[4,1,1,1,2] => 1
[4,1,1,2,1] => 1
[4,1,1,3] => 1
[4,1,2,1,1] => 1
[4,1,2,2] => 1
[4,1,3,1] => 1
[4,1,4] => 1
[4,2,1,1,1] => 0
[4,2,1,2] => 1
[4,2,2,1] => 0
[4,2,3] => 2
[4,3,1,1] => 0
[4,3,2] => 0
[4,4,1] => 0
[4,5] => 0
[5,1,1,1,1] => 0
[5,1,1,2] => 1
[5,1,2,1] => 1
[5,1,3] => 1
[5,2,1,1] => 0
[5,2,2] => 0
[5,3,1] => 0
[5,4] => 0
[6,1,1,1] => 0
[6,1,2] => 1
[6,2,1] => 0
[6,3] => 0
[7,1,1] => 0
[7,2] => 0
[8,1] => 0
[9] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,2,2] => 0
[1,1,1,1,2,1,1,2] => 1
[1,1,1,1,2,2,1,1] => 0
[1,1,1,1,3,3] => 0
[1,1,1,1,5,1] => 0
[1,1,2,1,1,1,1,2] => 1
[1,1,2,1,1,2,1,1] => 1
[1,1,2,1,2,3] => 1
[1,1,2,2,1,1,1,1] => 0
[1,1,2,2,2,2] => 0
[1,1,3,1,1,3] => 1
[1,1,3,2,1,2] => 1
[1,1,3,3,1,1] => 0
[1,1,4,4] => 0
[1,1,7,1] => 0
[1,2,1,1,4,1] => 1
[1,2,6,1] => 0
[1,3,1,1,3,1] => 1
[1,3,5,1] => 0
[1,4,1,1,2,1] => 1
[1,4,4,1] => 0
[1,5,1,1,1,1] => 0
[1,5,3,1] => 0
[1,6,1,2] => 1
[1,6,2,1] => 0
[1,7,1,1] => 0
[1,8,1] => 0
[1,9] => 0
[2,1,1,1,1,1,1,2] => 1
[2,1,1,1,1,2,1,1] => 1
[2,1,1,1,2,3] => 1
[2,1,1,2,1,1,1,1] => 1
[2,1,1,2,2,2] => 1
[2,1,2,1,1,3] => 2
[2,1,2,2,1,2] => 2
[2,1,2,3,1,1] => 1
[2,1,3,4] => 1
[2,1,6,1] => 1
[2,2,1,1,1,1,1,1] => 0
[2,2,1,1,2,2] => 1
[2,2,2,1,1,2] => 1
[2,2,2,2,1,1] => 0
[2,2,3,3] => 0
[3,1,1,1,1,3] => 1
[3,1,1,2,1,2] => 2
[3,1,1,3,1,1] => 1
[3,1,2,4] => 1
[3,2,1,1,1,2] => 1
[3,2,1,2,1,1] => 1
[3,2,2,3] => 2
[3,3,1,1,1,1] => 0
[3,3,2,2] => 0
[4,1,1,4] => 1
[4,2,1,3] => 1
[4,3,1,2] => 1
[4,4,1,1] => 0
[5,5] => 0
[8,1,1] => 0
[9,1] => 0
[1,10] => 0
[1,8,1,1] => 0
[1,7,2,1] => 0
[1,6,3,1] => 0
[1,5,4,1] => 0
[1,4,5,1] => 0
[1,3,6,1] => 0
[1,2,7,1] => 0
[1,1,8,1] => 0
[10,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,2,2] => 0
[1,1,1,1,1,1,2,2,1,1] => 0
[1,1,1,1,1,1,2,1,1,2] => 1
[1,1,1,1,1,1,3,3] => 0
[1,1,1,1,2,2,1,1,1,1] => 0
[1,1,1,1,2,2,2,2] => 0
[1,1,1,1,2,1,1,2,1,1] => 1
[1,1,1,1,2,1,1,1,1,2] => 1
[1,1,1,1,2,1,2,3] => 1
[1,1,1,1,3,3,1,1] => 0
[1,1,1,1,3,2,1,2] => 1
[1,1,1,1,3,1,1,3] => 1
[1,1,1,1,4,4] => 0
[1,1,2,2,1,1,1,1,1,1] => 0
[1,1,2,2,1,1,2,2] => 1
[1,1,2,2,2,2,1,1] => 0
[1,1,2,2,2,1,1,2] => 1
[1,1,2,2,3,3] => 0
[1,1,2,1,1,2,1,1,1,1] => 1
[1,1,2,1,1,2,2,2] => 1
[1,1,2,1,1,1,1,2,1,1] => 1
[1,1,2,1,1,1,1,1,1,2] => 1
[1,1,2,1,1,1,2,3] => 1
[1,1,2,1,2,3,1,1] => 1
[1,1,2,1,2,2,1,2] => 2
[1,1,2,1,2,1,1,3] => 2
[1,1,2,1,3,4] => 1
[1,1,3,3,1,1,1,1] => 0
[1,1,3,3,2,2] => 0
[1,1,3,2,1,2,1,1] => 1
[1,1,3,2,1,1,1,2] => 1
[1,1,3,2,2,3] => 2
[1,1,3,1,1,3,1,1] => 1
[1,1,3,1,1,2,1,2] => 2
[1,1,3,1,1,1,1,3] => 1
[1,1,3,1,2,4] => 1
[1,1,4,4,1,1] => 0
[1,1,4,3,1,2] => 1
[1,1,4,2,1,3] => 1
[1,1,4,1,1,4] => 1
[1,1,5,5] => 0
[2,2,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,2,2] => 1
[2,2,1,1,2,2,1,1] => 1
[2,2,1,1,2,1,1,2] => 2
[2,2,1,1,3,3] => 1
[2,2,2,2,1,1,1,1] => 0
[2,2,2,2,2,2] => 0
[2,2,2,1,1,2,1,1] => 1
[2,2,2,1,1,1,1,2] => 1
[2,2,2,1,2,3] => 1
[2,2,3,3,1,1] => 0
[2,2,3,2,1,2] => 1
[2,2,3,1,1,3] => 1
[2,2,4,4] => 0
[2,1,1,2,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,2,2] => 2
[2,1,1,2,2,2,1,1] => 1
[2,1,1,2,2,1,1,2] => 2
[2,1,1,2,3,3] => 1
[2,1,1,1,1,2,1,1,1,1] => 1
[2,1,1,1,1,2,2,2] => 1
[2,1,1,1,1,1,1,2,1,1] => 1
[2,1,1,1,1,1,1,1,1,2] => 1
[2,1,1,1,1,1,2,3] => 1
[2,1,1,1,2,3,1,1] => 1
[2,1,1,1,2,2,1,2] => 2
[2,1,1,1,2,1,1,3] => 2
[2,1,1,1,3,4] => 1
[2,1,2,3,1,1,1,1] => 1
[2,1,2,3,2,2] => 1
[2,1,2,2,1,2,1,1] => 2
[2,1,2,2,1,1,1,2] => 2
[2,1,2,2,2,3] => 1
[2,1,2,1,1,3,1,1] => 2
[2,1,2,1,1,2,1,2] => 3
[2,1,2,1,1,1,1,3] => 2
[2,1,2,1,2,4] => 2
[2,1,3,4,1,1] => 1
[2,1,3,3,1,2] => 2
[2,1,3,2,1,3] => 2
[2,1,3,1,1,4] => 2
[2,1,4,5] => 1
[3,3,1,1,1,1,1,1] => 0
[3,3,1,1,2,2] => 1
[3,3,2,2,1,1] => 0
[3,3,2,1,1,2] => 1
[3,3,3,3] => 0
[3,2,1,2,1,1,1,1] => 1
[3,2,1,2,2,2] => 1
[3,2,1,1,1,2,1,1] => 1
[3,2,1,1,1,1,1,2] => 1
[3,2,1,1,2,3] => 1
[3,2,2,3,1,1] => 2
[3,2,2,2,1,2] => 1
[3,2,2,1,1,3] => 1
[3,2,3,4] => 2
[3,1,1,3,1,1,1,1] => 1
[3,1,1,3,2,2] => 1
[3,1,1,2,1,2,1,1] => 2
[3,1,1,2,1,1,1,2] => 2
[3,1,1,2,2,3] => 1
[3,1,1,1,1,3,1,1] => 1
[3,1,1,1,1,2,1,2] => 2
[3,1,1,1,1,1,1,3] => 1
[3,1,1,1,2,4] => 1
[3,1,2,4,1,1] => 1
[3,1,2,3,1,2] => 2
[3,1,2,2,1,3] => 2
[3,1,2,1,1,4] => 2
[3,1,3,5] => 1
[4,4,1,1,1,1] => 0
[4,4,2,2] => 0
[4,3,1,2,1,1] => 1
[4,3,1,1,1,2] => 1
[4,3,2,3] => 2
[4,2,1,3,1,1] => 1
[4,2,1,2,1,2] => 2
[4,2,1,1,1,3] => 1
[4,2,2,4] => 2
[4,1,1,4,1,1] => 1
[4,1,1,3,1,2] => 2
[4,1,1,2,1,3] => 2
[4,1,1,1,1,4] => 1
[4,1,2,5] => 1
[5,5,1,1] => 0
[5,4,1,2] => 1
[5,3,1,3] => 1
[5,2,1,4] => 1
[5,1,1,5] => 1
[6,6] => 0
-----------------------------------------------------------------------------
Created: May 18, 2017 at 09:37 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Jan 11, 2018 at 10:01 by Martin Rubey